If the expression `(1 + ir)^3` is of the form of `s(1+ i)` for some real 's' where 'r' is also real and `i = sqrt(-1)`

" 2.Express "(1-i)^(3)(1+i)" in the form of "a+ib

if cos (1-i) = a+ib, where a , b in R and i = sqrt(-1) , then

Perform the indicated operation and give your anwer in the form x+iy , where x and y are real numbers and i=sqrt(-1) : (i) ((1)/(2)+(1)/(4)i)(-(2)/(3)-(1)/(4)i) (ii) (5+2i)/(-1+sqrt(3)i) . (iii) (sqrt(5)-7i)(sqrt(5)-7i)^(2)+(-2+7i)^(2) .

Find the set of points on the argand plane for which the real part of the complex number (1 + i)z^2 is positive where z = x + iy, x , y in R and i = sqrt(-1 ) .

Put the complex number (1+7i)/((2-i)^(2)) in the form r(cos theta+is int h eta) where r is a positive real number and * pi

If the complex numbers is (1+ri)^(3)=lambda(1+i) , when i=sqrt(-1) , for some real lambda , the value of r can be

Express (1+i)^(-1) ,where, i= sqrt(-1) in the form A+iB.